1
JEE Main 2020 (Online) 3rd September Morning Slot
+4
-1
A block of mass m = 1 kg slides with velocity v = 6 m/s on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about O and swings as a result of the collision making angle $$\theta$$ before momentarily coming to rest. If the rod has mass M = 2 kg, and length $$l$$ = 1 m, the value of $$\theta$$ is approximately :
(take g = 10 m/s2)
A
63o
B
69o
C
55o
D
49
2
JEE Main 2020 (Online) 2nd September Morning Slot
+4
-1
A particle of mass m with an initial velocity $$u\widehat i$$ collides perfectly elastically with a mass 3 m at rest. It moves with a velocity $$v\widehat j$$ after collision, then, v is given by :
A
$$v = \sqrt {{2 \over 3}} u$$
B
$$v = {u \over {\sqrt 3 }}$$
C
$$v = {u \over {\sqrt 2 }}$$
D
$$v = {1 \over {\sqrt 6 }}u$$
3
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
A rod of length L has non-uniform linear mass
density given by $$\rho$$(x) = $$a + b{\left( {{x \over L}} \right)^2}$$ , where a
and b are constants and 0 $$\le$$ x $$\le$$ L. The value
of x for the centre of mass of the rod is at :
A
$${3 \over 2}\left( {{{a + b} \over {2a + b}}} \right)L$$
B
$${4 \over 3}\left( {{{a + b} \over {2a + 3b}}} \right)L$$
C
$${3 \over 4}\left( {{{2a + b} \over {3a + b}}} \right)L$$
D
$${3 \over 2}\left( {{{2a + b} \over {3a + b}}} \right)L$$
4
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
A particle of mass m is projected with a speed u from the ground at an angle $$\theta = {\pi \over 3}$$ w.r.t. horizontal (x-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity $$u\widehat i$$ . The horizontal distance covered by the combined mass before reaching the ground is:
A
$$2\sqrt 2 {{{u^2}} \over g}$$
B
$${{3\sqrt 3 } \over 8}{{{u^2}} \over g}$$
C
$${{3\sqrt 2 } \over 4}{{{u^2}} \over g}$$
D
$${5 \over 8}{{{u^2}} \over g}$$
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